How do you power it? I know you can use a higher voltage PSU and the system will take what it needs, but does it regulate the voltage at some point?

I want to use a 12v screen with a 9v PC Engine. Just considering that this could be a problem.

Same for me
Hopefully my ordered screen is satisfied with something like 9V as mentioned here:
viewtopic.php?t=42870

Bad idea! You're confusing Volts and Amps. More Volts may kill the console. It will only draw the Amps it needs if provided the correct voltage.

Less Volts may work for the screen, but do not hook 12V to the PC Engine, at least until it's determined that it has a voltage regulator internally and what its range is.

If the screen uses the old-style CCFL backlights, then it may not run on much less voltage, as those backlights tend to require high voltage.

However, if it's LED backlit, then it should be regulated somewhere, which you might have to replace/bypass.

Really? I know for my Megadrive, I can use 12V and it will power up fine. I think I've stuck 9V through a 3V Gameboy Pocket too, and it did no harm. Don't know what a voltage regulator looks like. aha. Yes, there is one, and I know exactly where it is. I thought that was an old transistor! Considering where it is, I expect there is space to get 12V from the PSU before the regulator.

And the LCD is the new type.

Not all regulators are fixed output. Check the numbers on it and see the datasheet for it. If it's a 7805, and the voltage doesn't go anywhere else, you'll be fine with putting in 12V then. A great many electronics have regulators that can take a good range of voltages, but not all.

This thread is perfect timing for me to ask a stupid question I've powered a Yobo NES at a 6v minimum, but used a 9v adapter as well. I'm guessing a 12v power supply would fry it?

Probably. How is a thread that was posted several months ago 'perfect timing'?